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Expected Value

Expected Value

The expected value is known as the "long-term" average or mean. This means that over the long term of experimenting over and over, you would expect this average. The expected average is represented by the symbol μ. It is calculated as follows:In the equation, x is an event, and P(x) is the probability of the event occurring.The expected value has practical applications in decision theory.This text is adapted from Openstax, Introductory Statistics, Section 4.2 Mean or Expected Value and...

Expected Frequencies in Goodness-of-Fit Tests

Expected Frequencies in Goodness-of-Fit Tests

A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (n) to the number of categories (k).

Determination of Expected Frequency

Determination of Expected Frequency

Suppose one wants to test independence between the two variables of a contingency table. The values in the table constitute the observed frequencies of the dataset. But how does one determine the expected frequency of the dataset? One of the important assumptions is that the two variables are independent, which means the variables do not influence each other. For independent variables, the statistical probability of any event involving both variables is calculated by multiplying the individual...

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...

Decision Making: P-value Method

Decision Making: P-value Method

The process of hypothesis testing based on the P-value method includes calculating the P- value using the sample data and interpreting it.
First, a specific claim about the population parameter is proposed. The claim is based on the research question and is stated in a simple form. Further, an opposing statement to the claim is also stated. These statements can act as null and alternative hypotheses: a null hypothesis would be a neutral statement while the alternative hypothesis can have a...

Estimation of the Physical Quantities

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On many occasions, physicists, other scientists, and engineers need to make estimates of a particular quantity. These are sometimes referred to as guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. The physicist Enrico Fermi was famous for his ability to estimate various kinds of data with surprising precision. Estimating does not mean guessing a number or a formula at random. Instead, estimation means using prior experience and sound...

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Related Experiment Video

Updated: May 12, 2026

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods

Published on: September 19, 2012

Need for speed: an efficient algorithm for calculation of single-parameter expected value of partial perfect

Mohsen Sadatsafavi¹, Nick Bansback, Zafar Zafari

¹Department of Medicine, University of British Columbia, Vancouver, BC, Canada. mohsen.sadatsafavi@alumni.ubc.ca

Value in Health : the Journal of the International Society for Pharmacoeconomics and Outcomes Research

|March 30, 2013

Summary

A new, efficient one-level simulation method significantly speeds up the calculation of the expected value of partial perfect information (EVPPI) in cost-effectiveness models. This approach offers a faster and more accurate way to assess uncertainty for single parameters.

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Area of Science:

Decision Analysis
Health Economics
Computational Statistics

Background:

The expected value of partial perfect information (EVPPI) is crucial for quantifying uncertainty in cost-effectiveness models.
Traditional EVPPI calculation involves computationally intensive two-level Monte Carlo simulations.
A need exists for more efficient methods to compute EVPPI, especially for single parameters.

Purpose of the Study:

To introduce and validate an efficient one-level simulation method for calculating single-parameter EVPPI.
To demonstrate the transformation of the EVPPI calculation sequence from expectation-maximization-expectation to expectation-maximization-maximization.
To prove the convergence of the proposed EVPPI estimator.

Main Methods:

Developed a novel one-level simulation approach for EVPPI calculation.
Utilized data from probabilistic sensitivity analysis for single-step expectation calculations.
Empirically tested the method on three decision models.

Main Results:

The proposed one-level method achieves higher accuracy compared to the two-level method at a fraction of the computational cost.
Accuracy improvements varied across different model parameters.
Provided software for calculating single-parameter EVPPI using probabilistic sensitivity analysis data.

Conclusions:

The new method offers a fast, accurate, and implementable solution for single-parameter EVPPI calculation.
Further research is recommended to extend this methodology to more complex decision uncertainty measures and scenarios.